September 23rd - Powers of Ten, Sig Digs, and More!

On September 22, scientists at CERN announced that they had recorded particles moving faster than the speed of light. They say that if their claim is correct, they may have disproved Einstein's Theory of Special Relativity, which states that nothing can travel faster than light. In their experiment, they recorded neutrinos arriving 60 nanoseconds before light at a detector in Gran Sasso, Italy. The sixty nanosecond (10^-9) difference is a significant number, as we learned in the previous section. If confirmed true, this would force physicists to rethink much that they know about the universe.

Some sources believe that Einstein’s theory of relativity can be broken. It states that nothing can travel at the speed of light. Assuming that neutrinos are in fact faster, their findings would be very difficult to explain. How can it be possible to go from 5 m/s to 7m/s without passing through 6 m/s? We look forward to hearing from other science labs that are currently trying to replicate the experiment.

Now back to chemistry! We began by learning about the magnitude of powers of ten. Each time you move down a power of ten (ie. From 10¹⁰ to 10⁹) you lose 90% of whatever you are measuring. One notable power of ten is 10¹⁶ metres, which is a light-year This is followed by 10¹⁷ metres, which is ten light-years. Another interesting power is 10^-10, which is an angstrom.

This interesting video gives us a sense of how big or small these numbers really are:

The next topic we covered was significant digits. We were given a worksheet and were instructed to complete it. Some important ideas about significant digits are:

• Any non-zero number is significant (ie. 456 has 3 significant digits)
• Zeroes that aren’t place keepers are significant (ie. 304 has 3 significant digits)
• Estimated zeroes are significant (ie. 1.040 has 4 significant digits)

Note: The number 4000 has four significant digits. When we see a whole number with multiple zeroes, we should assume there is a decimal place after the last zero. This decimal place indicates that the zeroes are significant digits (they are part of the measurement). If the number was written in the form 4 x 10³, it would have one significant digit.

To determine the number of significant digits when adding or subtracting, follow these steps:

1. Add or subtract as you normally would
2. Determine the lowest decimal position of the original numbers
3. Round your answer to that decimal position

ie. 3.1 + 2.11 = 5.21. The lowest decimal position of the original numbers is in the tenths spot, so the answer is rounded to 5.2.

To determine the number of significant digits when multiplying or dividing:

1. Multiply or divide as you normally would
2. Find the number with the lowest number of significant digits of the original numbers
3. Round your answer, making sure that the answer has the same number of significant digits as the number from the second step

ie. 2 x 1.25 = 2.5. The lowest number of significant digits in the original numbers is 1, so we round the answer to 3.

We concluded the lesson with a few examples of scientific notation. To recall, a number written in proper scientific notation is between 1 and 9 (inclusive) and written to an according power.

What can this be?

 

A neutrino of course!

Posted by Andrew.